Sample Exercises  
Chapter 6: Applications of Trigonometric Functions 
 
  1. As you are approaching a mountain in your car you notice a sign that states, "CAUTION STEEP SLOPE AHEAD --- 10% GRADE."  The 10% grade means that the road has a slope of 0.10 or every time the horizontal distance changes by 10 feet, the vertical distance changes by one foot.
    1. As you start driving up the mountain, what is your angle of elevation?
    2. If, according to your odometer, you have driven up the mountain for 2 miles (10,560 feet), what is your increase in elevation?
     
  1. The Measurement Guidelines set by The South Dakota Register of Big Trees says that one way of measuring the height of a tree is to do the following:
    2. Use a stick whose length is the same as the length of your arm.  Hold the stick vertically at arm's length and walk backwards away from the tree until the stick above your hand appears to be the same length as the tree.  Measure how far you have backed away from the tree.  This  measurement is approximately equal to the height of the tree.
    Explain why this method works.
     
  2. Use the law of sines to prove: The base angles of an isosceles triangle are congruent.
  1. A Calculator-Based Ranger (CBR) connected to a graphing calculator was used to graph the path of a slow moving toy truck as it passed through the path of the CBR beam. The CBR emits a cone-shaped sonic beam at an angle of 20°. The time from when the ultrasonic pulses are emitted and when the first echo is returned is used to calculate the distance an object is away from the CBR. The calculator gives the time when the truck entered the beam and its distance from the CBR as well as the time when the truck left the beam and its distance from the CBR. Using the data collected on the calculator, you will be asked to calculate the speed of the truck. In the following figure, side AB indicates that the truck was 18.0 inches from the CBR when it entered the beam. Side AC indicates that the truck was 25.3 inches from the CBR when it left the beam. Side BC represents the distance the truck traveled.
    1. Find the length of BC.
    2. The truck entered the beam after the program was running for 17.4 seconds and exited the beam after the program was running for 49.0 seconds. Using this, find the speed of the truck in inches per second.
     
  1. The following table contains the average low temperature in degrees Fahrenheit (from 1961 to 1990) for Milwaukee, Wisconsin.

    2.  
    Month Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec.
    Temperature 11.6° 15.9° 26.2° 35.8° 44.8° 55.0° 62.0° 60.8° 52.8° 41.8° 30.7° 17.5°
     
    1. Find a function, L, which models the data where m is the month (January = 1, February = 2, etc.) and L(m) is the average low temperature.
    2. Suppose that the average high temperature was typically 20° higher than the average low temperature.  Find a function, H, which models the average high temperature.
    3. Suppose you wanted a function whose output was in Celsius rather than Fahrenheit.  Find a function, C, which models the average low temperature in Celsius.
                [Note:  The formula to convert from Fahrenheit to Celsius is C = (5/9)(F - 32).]

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